Synthetic dimensions for cold atoms from shaking a harmonic trap

Hannah M. Price, Tomoki Ozawa, Nathan Goldman

Research output: Contribution to journalArticlepeer-review

68 Citations (Scopus)


We introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realization of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.

Original languageEnglish
Article number023607
JournalPhysical Review A
Issue number2
Publication statusPublished - 2017 Feb 9


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